
<h1><span class="yiyi-st" id="yiyi-12">numpy.linalg.eigvals</span></h1>
        <blockquote>
        <p>原文：<a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eigvals.html">https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eigvals.html</a></p>
        <p>译者：<a href="https://github.com/wizardforcel">飞龙</a> <a href="http://usyiyi.cn/">UsyiyiCN</a></p>
        <p>校对：（虚位以待）</p>
        </blockquote>
    
<dl class="function">
<dt id="numpy.linalg.eigvals"><span class="yiyi-st" id="yiyi-13"> <code class="descclassname">numpy.linalg.</code><code class="descname">eigvals</code><span class="sig-paren">(</span><em>a</em><span class="sig-paren">)</span><a class="reference external" href="http://github.com/numpy/numpy/blob/v1.11.3/numpy/linalg/linalg.py#L832-L918"><span class="viewcode-link">[source]</span></a></span></dt>
<dd><p><span class="yiyi-st" id="yiyi-14">计算一般矩阵的特征值。</span></p>
<p><span class="yiyi-st" id="yiyi-15"><a class="reference internal" href="#numpy.linalg.eigvals" title="numpy.linalg.eigvals"><code class="xref py py-obj docutils literal"><span class="pre">eigvals</span></code></a>和<a class="reference internal" href="numpy.linalg.eig.html#numpy.linalg.eig" title="numpy.linalg.eig"><code class="xref py py-obj docutils literal"><span class="pre">eig</span></code></a>之间的主要区别：不返回本征向量。</span></p>
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<tr class="field-odd field"><th class="field-name"><span class="yiyi-st" id="yiyi-16">参数：</span></th><td class="field-body"><p class="first"><span class="yiyi-st" id="yiyi-17"><strong>a</strong>：（...，M，M）array_like</span></p>
<blockquote>
<div><p><span class="yiyi-st" id="yiyi-18">将计算其特征值的复值或实值矩阵。</span></p>
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<tr class="field-even field"><th class="field-name"><span class="yiyi-st" id="yiyi-19">返回：</span></th><td class="field-body"><p class="first"><span class="yiyi-st" id="yiyi-20"><strong>w</strong>：（...，M，）ndarray</span></p>
<blockquote>
<div><p><span class="yiyi-st" id="yiyi-21">特征值，每个根据其多重性重复。</span><span class="yiyi-st" id="yiyi-22">它们不一定是有序的，也不一定是真实的矩阵。</span></p>
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<tr class="field-odd field"><th class="field-name"><span class="yiyi-st" id="yiyi-23">上升：</span></th><td class="field-body"><p class="first"><span class="yiyi-st" id="yiyi-24"><strong>LinAlgError</strong></span></p>
<blockquote class="last">
<div><p><span class="yiyi-st" id="yiyi-25">如果特征值计算不收敛。</span></p>
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<div class="admonition seealso">
<p class="first admonition-title"><span class="yiyi-st" id="yiyi-26">也可以看看</span></p>
<dl class="last docutils">
<dt><span class="yiyi-st" id="yiyi-27"><a class="reference internal" href="numpy.linalg.eig.html#numpy.linalg.eig" title="numpy.linalg.eig"><code class="xref py py-obj docutils literal"><span class="pre">eig</span></code></a></span></dt>
<dd><span class="yiyi-st" id="yiyi-28">一般数组的特征值和右特征向量</span></dd>
<dt><span class="yiyi-st" id="yiyi-29"><a class="reference internal" href="numpy.linalg.eigvalsh.html#numpy.linalg.eigvalsh" title="numpy.linalg.eigvalsh"><code class="xref py py-obj docutils literal"><span class="pre">eigvalsh</span></code></a></span></dt>
<dd><span class="yiyi-st" id="yiyi-30">对称或Hermitian数组的特征值。</span></dd>
<dt><span class="yiyi-st" id="yiyi-31"><a class="reference internal" href="numpy.linalg.eigh.html#numpy.linalg.eigh" title="numpy.linalg.eigh"><code class="xref py py-obj docutils literal"><span class="pre">eigh</span></code></a></span></dt>
<dd><span class="yiyi-st" id="yiyi-32">对称/ Hermitian数组的特征值和特征向量。</span></dd>
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<p class="rubric"><span class="yiyi-st" id="yiyi-33">笔记</span></p>
<div class="versionadded">
<p><span class="yiyi-st" id="yiyi-34"><span class="versionmodified">版本1.8.0中的新功能。</span></span></p>
</div>
<p><span class="yiyi-st" id="yiyi-35">广播规则适用，有关详细信息，请参阅<code class="xref py py-obj docutils literal"><span class="pre">numpy.linalg</span></code>文档。</span></p>
<p><span class="yiyi-st" id="yiyi-36">这是使用_geev LAPACK例程来实现的，其计算一般方阵数组的特征值和特征向量。</span></p>
<p class="rubric"><span class="yiyi-st" id="yiyi-37">例子</span></p>
<p><span class="yiyi-st" id="yiyi-38">Illustration, using the fact that the eigenvalues of a diagonal matrix are its diagonal elements, that multiplying a matrix on the left by an orthogonal matrix, <em class="xref py py-obj">Q</em>, and on the right by <em class="xref py py-obj">Q.T</em> (the transpose of <em class="xref py py-obj">Q</em>), preserves the eigenvalues of the “middle” matrix. </span><span class="yiyi-st" id="yiyi-39">换句话说，如果<em class="xref py py-obj">Q</em>是正交的，则<code class="docutils literal"><span class="pre">Q</span> <span class="pre">*</span> <span class="pre">A</span> <span class="pre">t5&gt; <span class="pre">QT</span></span></code>具有与<code class="docutils literal"><span class="pre">A</span></code>相同的特征值：</span></p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">numpy</span> <span class="k">import</span> <span class="n">linalg</span> <span class="k">as</span> <span class="n">LA</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">()</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Q</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">)],</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="p">)]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">LA</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">Q</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:]),</span> <span class="n">LA</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">Q</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:]),</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">Q</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:],</span><span class="n">Q</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:])</span>
<span class="go">(1.0, 1.0, 0.0)</span>
</pre></div>
</div>
<p><span class="yiyi-st" id="yiyi-40">现在将一个对角矩阵乘以一侧的Q，另一侧乘以Q.T：</span></p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">D</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">((</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">LA</span><span class="o">.</span><span class="n">eigvals</span><span class="p">(</span><span class="n">D</span><span class="p">)</span>
<span class="go">array([-1.,  1.])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">Q</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">Q</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">LA</span><span class="o">.</span><span class="n">eigvals</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="go">array([ 1., -1.])</span>
</pre></div>
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</dd></dl>
